What is 5/54 plus 6/21? (Answer: 143/378)

Exact Answer

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Problem: What is 5/54 plus 6/21?
Formula / Expression: 5/54 + 6/21
Final Answer: 143/378
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 54 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 378 (which is smaller than their product 54 × 21 = 1134, keeping the calculation simpler).
Working: LCD(54, 21) = 378

Step 2: Convert to Equivalent Fractions with Common Denominator 378
Multiply the numerator and denominator of 5/54 by 7, and multiply the numerator and denominator of 6/21 by 18 so both fractions share the common base 378.
Working: 5 × 7/54 × 7 = 35/378 and 6 × 18/21 × 18 = 108/378

Step 3: Add the Numerators
Now add the numerators (35 + 108 = 143) and keep the common denominator 378 unchanged.
Working: 35 + 108/378 = 143/378

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 143 and 378 is 1, confirming that 143/378 cannot be reduced further—it is already in its simplest irreducible form.
Working: 143/378

Step 5: Decimal & Percentage Representation
Dividing the numerator 143 by denominator 378 produces a repeating decimal (approximately 0.378307, or 37.8307%).
Working: 143 ÷ 378 = 0.378307 (37.8307%)

Key Values:
- Simplified Fraction: 143/378
- Mixed Number Form: 143/378
- Decimal Value: 0.378307
- Percentage: 37.8307%

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5/54 + 6/21 = 143/378

Simplified Fraction

143/378

Mixed Number

Proper (143/378)

Decimal Value

0.378307

Percentage

37.8307%

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Step-by-Step Solution: 5/54 + 6/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 54 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 378 (which is smaller than their product 54 × 21 = 1134, keeping the calculation simpler).

LCD(54, 21) = 378

Step 2

Convert to Equivalent Fractions with Common Denominator 378

Multiply the numerator and denominator of 5/54 by 7, and multiply the numerator and denominator of 6/21 by 18 so both fractions share the common base 378.

5 × 7/54 × 7 = 35/378 and 6 × 18/21 × 18 = 108/378

Step 3

Add the Numerators

Now add the numerators (35 + 108 = 143) and keep the common denominator 378 unchanged.

35 + 108/378 = 143/378

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 143 and 378 is 1, confirming that 143/378 cannot be reduced further—it is already in its simplest irreducible form.

143/378

Step 5

Decimal & Percentage Representation

Dividing the numerator 143 by denominator 378 produces a repeating decimal (approximately 0.378307, or 37.8307%).

143 ÷ 378 = 0.378307 (37.8307%)

Visual Representation

The diagram below illustrates 5/54 plus 6/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`143/378`
Mixed Number Form	`143/378`
Decimal Form	`0.378307`
Percentage	`37.8307%`

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Frequently Asked Questions

What is 5/54 plus 6/21 as a fraction?

5/54 + 6/21 in simplest fraction form is 143/378.

What is 5/54 plus 6/21 as a decimal?

5/54 + 6/21 converted to a decimal is 0.378307.

What is 5/54 plus 6/21 as a percentage?

5/54 + 6/21 expressed as a percentage is 37.8307%.

Does 5/54 plus 6/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.378307...) because the denominator contains prime factors other than 2 and 5.